W. 0. MILLIGANAND HENRYH. RACHFORD, JR.
2922
[CONTRIBUTION FROM
THE
VOl. 70
DEPARTMENT O F CHEMISTRY, THERICE INSTITUTE]
The Sorption-Desorption Hysteresis Characteristics of the System Si02-H20Below the Bulk Freezing Point of Water1 BY w. 0 . MILLIGANAND HENRYH. RACHFORD, JR."~ The properties of sorbed materials may be in general quite different from those associated with the same materials under bulk conditions. This fact is of especial significance when sorption is considered to result from capillary condensation, since condensate in the pores might be expected to resemble closely a three-dimensional liquid. However, experimental observations indicate that even in such a system, differences between the capillary phase and the bulk phase are pronounced. The most striking differences appear to be (a) an abnormally low vapor pressure, (b) the absence of irregularities a t the critical temperature and (c) a depressed freezing point. There are reported in the literature4-I0 a number of investigations designed to determine the effect of capillary condensation on sorbate properties. I n no case mere there detected discontinuities or irregularities in the isotherms at the critical temperature. More recently Brunauer and Emmett in unpublished work (cf. ref. 8) found "that acetylene adsorption curves on iron catalyst for the synthesis of ammonia are the same over the range - 78' to - 100' when plotted on a relative pressure basis (using the extrapolated vapor pressure curve of liquid acetylene for PO),even though Other the melting point of acetylene is - 8 1 . 5 O . " investigators deduced from dilatometric measurements11p12and heats of fusionI3 that sorbed liquids behave abnormally below their bulk freezing point. A different point of view was developed by K ~ b e 1 k a . l ~By combining the expression developed by Riel5 and others for the lowering of melting points of finely divided crystalline solids with well known properties of gels, Kubelka derived an expression (T,
where
Tm
- T ) / T m=
(ZVu/rq) cos+
is the normal melting point of the sor-
(1) Presented before the Division of Colloid Chemistry a t the 110th meeting of the American Chemical Society, which was held in Chicago, Illinois, September 9-13, 1946. (2) Humble Oil and Refining Company Fellow in "X-Ray Diffraction Research" a t T h e Rice Institute, 1945-1946. (3) Present address: Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts. ( 4 ) Patrick, Preston and Owens, J . P h y s . Chem., 29, 421 (1925). (5) Morrisand Maass, Can. J . Reseavch, 9, 240 (1933). (6) Edwards and Maass, ibid., 13B, 133 (1935). (7) Brunauer, E m m e t t and Teller, THISJOURNAL, 60,309 (1938). ( 8 ) Emmett and Cines, J . Phys. Colloid Chem., 61, 1261 (1947). JOURNAL, 46,596 (1924). (9) Coolidge, THIS (10) Patrick and Land, J . Phys. Chem., 38, 1201 (1934). (11) Foote and Saxton. THISJ O U R N A L , 39, 1103 (1917). (12) Jones and Gortner, J. Phys. Chem., 36,387 (1932). (13) Patrick and Kemper, ibid., 42, 369 (1938). (14) Kubelka, Z . Elektvochern., 38, 611 (1932). (15) Rie, Z . p h y s i k . Chefn., 104,384 (1923).
bate, T the melting point of the sorbed material, V the molal volume of the liquid, r the capillary radius, p the heat of fusion, u the solid-liquid interfacial energy, and 4 the angle of contact of the liquid with the gel material. Experimental In view of the evidence that materials in the sorbed condition may not undergo phase transitions a t or near the bulk freezing point, it was believed that further observations to compare certain properties of the sorbate with those of the solid and liquid forms would be useful. For this study there was selected a series of silica gels whose sorption characteristics above the normal melting point of the sorbate had already been investigated in some detail.16 In the present work, the water sorption-desorption isotherms for these gels were studied a t - 5 " for comparison with results of the similar measurements carried out previously a t 12'. Preparation of Samples.-A detailed description of the samples has been given in a previous paper.16 The sorbent consisted of an air-dry silica gel heated in air for two hours a t the fo1lowi:g temperatures, respectively : 450,500, 650, 725 and 880 . Following the heat treatment the samples were placed in a n air stream saturated with water vapor a t room temperature (30"),and finally sorptiondesorption isotherms were obtained a t 12".16 These identical gels were then examined a t - 5 O as described below. Apparatus.-The isotherms for the five samples were measured a t - 5 " in a multiple apparatus described in a previous report from this Laboratory.'' T h t temperature was held constant to better than +0.005 . During the initial degassing period of twenty-four hours, the samples came to equilibrium a t a pressure not exceeding mm. At the end of the evacuation period the vacuum system was closed off and air-free water vapor (from the thermal decomposition of degassed BaC12.2H20) was pumped intermittently into the manifold containing the gels; sufficient time was allowed after each pressure increase to ensure that the system attained equilibrium. The weight of water sorbed on 100-mg. samples of dry gel was determined with a precision of 0.01 mg. by the change in deflection of McBain-Bakr silica spring balances. The prevailing pressure was read by means of an oil manometer to within 0.01 cm. of oil, corresponding to 0.004 p / p unit. ~ The isotherms ( x / m versus p/po) taking PO equal t o the saturated vapor pressure of supercooled water, are shown in Figs. 1-5. I n the same figures are plotted the corresponding uncorrected frequency distribution curves, (bV/br)T, versus r ( V is the volume of sorbate, referred to liquid conditions, and Y is the capillary radius).
Discussion A comparison of the isotherms a t -5' with those at 12' reveals that the curves are almost identical if the saturated vapor pressure of supercooled water rather than that of ice is used in plotting. Of necessity p can never reach PO because of the intervening condensation pressure of ice, hence there is a variation in behavior a t values above $/POequal to 0.9. In order t o examine more closely the possible (16) Milligan and Rachford, J. P h y s . Colloid C h e m . , 51,333 (1947). (17) Simpson, "Thesis," T h e Rice Institute, Houston, Texas, 1943.
SORPTION-DESORPTION OF SILICA-WATER SYSTEM
Sept., 1048 1.0
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8.
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0.8
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0.6
-
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0.8
PIP&
@/PO.
Fig. 1.-Sorption-desorptbn isotherm a t -5' for silica gel heat-treated at 450
'.
Fig. 3.-Sorption-desorption isotherm at -5' gel heat-treated a t 650'.
1.0 I
i
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for silica
1-
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0.8
I
4 t
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PIP,. Fig. 2.-Sorption-desorption isotherm a t gel heat-treated a t 500".
0.0 0.0
0.8
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PIPO.
-5'
for silica
differences between the isotherms a t -5' and 1 2 O , the data were plotted as V versus r using the &Ivin equatibn (15) In P - In po = -2yVjrRT where y is the surface tension of supercooled water, V the molal liquid volume, R the gas constant and T the absolute temperature. From this logarithmic relation the frequency distribution curves were derived. The respective peaks in these curves seem to approach very closely those obtained from the 12' isothems,l6 appearing a t virtually the same value of r (ca. 28.5 A) and having strikingly similar shapes. It is believed that the data obtained in the present set of isotherms constitutes independent veri-
Fig. 4.-Sorption-desorption isotherm a t -5' gel heat-treated at.725'.
for silica
fication of the fact that a t least in some cases the melting point of sorbed materials may be considerably lower than the bulk value. In addition it is interesting that a close correlation between the frequency distribution curve from isotherms a t 12' and - 5' results from the use of a saturation pressure corresponding to the experimentally determined vapor pressure of supercooled water a t the temperature, while the correlation is poor using po as the vapor pressure of ice. The facts illustrated by the data suggest a method for estimating the minimum value possible for the sorbate freezing point in the system studied. From the form of the Kubelka equation we may infer that for sufficiently small values of r, or large values of u there will exist no temperature a t
‘924
M’. 0. LIILLIGAN ...-
AND
HENRYH.
KACHFORD, JR.
VOl. $0
Under these circumstances, the vapor pressure of water in the pores will be exactly equal to the vapor pressure of bulk solid ice a t the same temperai ture. Any subsequent lowering of the temperature 0.8 I I &--I 41 (solid ice remaining present in equilibrium) would be expected to dehydrate the pores as the vapor condenses in the bulk solid form, which a t that temperature is of lower vapor pressure. During melting, the process must be reversed; from the hysteresis in the isotherms i t appears evident that a higher PO (and thus a higher temperature) will be required to recondense water into the pores. This would account for the hysteresis observed by Jones and Gortner.6 A comparison of the extrapolated liquid vapor pressure of water with that of ice shows that to oh tain ice a t $/PO of 0.7 (the value corresponding to the pressure exerted by the water condensed in the 0.0 0.2 0.4 0.6 0.8 majority of the pores) the temperature must be -37’. This would seem to correspond to a “freezPIPO. Fig. 5.-Sorption-desorption isotherm at -5’ for silica ing point.” For melting, the p/po value must then be raised to 0.8 (corresponding to the relative presgel heat-treated a t 880”. sure a t which most of the pores become saturated) which the sorbate within the pores will be solid. with a “required melting point” temperature of Inasmuch as there is a t hand no reliable means of - 2 1 O . It should be emphasized that the temperatures measuring the interfacial energy between liquid water and ice, i t is impossible a t present to predict calculated by this method represent a lower limit a t what apparent pore radius such a condition will for the sorbate freezing or melting point, since the obtain. However, since in the present discussion analysis is developed on the assumption that liqwe are estimating the minimum possible “freezing uid sorbed by capillary condensation in the pores point,” a hypothesis will be considered from which will not freeze. the Kubelka equation indicates either a very low, Summary or even non-existent value for T. For the system Experimental work reported in the literature at hand the validity of such an assumption does not seem unreasonable from a consideration of the has shown that substances in the sorbed condition relative orders of magnitude of the factors in the held by so-called capillary condensation forces, equation, taking r as 28.5 X loF8 crn. These con- may not exhibit anomalous behavior as the temsiderations suggest the possibility of freezing the perature is allowed to vary through values a t capillary-condensed liquid a t a temperature higher which phase transitions in the bulk condition northan T , the freezing point temperature from the mally occur. To study further this behavior, a Kubelka equation. This would take place as will set of sorption-desorption isotherms for water vabe described below by means of a somewhat dif- por on several silica gels was measured a t -5’. ferent mechanism from that associated with the The sorption characteristics of the same samples assumptions governing the Kubelka equation. had previously been determined a t 12’ so that a Inasmuch as the vapor pressure of supercooled wa- comparison showing the effect of subfreezing temter is greater than that of ice, the isotherm below peratures on the isotherm could be made. It was 0’ is found always to break down with attendant found that when the sorption was plotted against ice formation a t some value of p/po (90 being based the relative saturation, the isotherms a t the two on the value for supercooled water) less than one. temperatures coincided only if the satufation presAs the temperature is decreased, since the diver- sure was taken to be the experimentally detergence between the water and ice vapor pressures mined value for supercooled water a t that temperincreases with decreasing temperature, the p / p o ature. On this basis there is suggested a procedure value at which the solid bulk sorbate forms in the for the estimation of the minimum possible “freezapparatus also decreases. At some temperature ing” and “melting” points, which would yield an an ice point value of $/PO will be reached that cor- explanation of observed freezing-melting hystereresponds to the vapor pressure of water condensed sis phenomena consistent with the hysteresis obin the pores of radius r, the radius a t which the served in the sorption-desorption isotherms. peak in the frequency distribution curve occurs. HOUSTON,TEXAS RECEIVEDMAY18, 1948 10
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